package leetcode.l0613;

import java.util.HashSet;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.ThreadLocalRandom;

/**
 * 给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
 * @author Retain
 * @date 2021/6/13 19:18
 */
public class Medium_最小路径和_64 {

    public static void main(String[] args) {
        minPathSum(new int[][]{{1,3,1},{1,5,1},{4,2,1}});
    }
    /**
     * 跟上面的题很相似
     * 同样dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1])+grid[i][j] 表示到i,j最小的路径
     * @param grid
     * @return
     */
    public static int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        //初始化dp[][]
        dp[0][0] = grid[0][0];
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i-1]+grid[0][i];
        }
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i-1][0]+grid[i][0];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1]) + grid[i][j];
            }
        }
        return dp[m-1][n-1];
    }
}
